Displacement-Parameter Weighted Coordinate Comparison: I. Detection of Significant Structural Differences Between Oxidation States

Abstract

A method, displacement-parameter weighted coordinate comparison, for comparing closely related structures is developed. A 'probability of similarity' is derived from the overlap between the most probable volumes occupied by two analogous atoms in a comparison. The distribution of distances between atom pairs (difference distances), where each distance is weighted by the probability of similarity, is examined. The subset of atom pairs with normally distributed difference distances is used to estimate errors in the difference distances and to calculate the probability that the difference is significant for each atom-pair. These probabilities of difference are shown to correlate with features observed in difference maps for diffraction data from oxidized and reduced forms of the cupredoxin, pseudoazurin. The pair-wise probability of difference also is shown to be correlated with regions in previously published plastocyanin structures which differ upon copper oxidation state change, and which differ in a similar manner when temperature is changed, or pH is changed.

Reliability of atomic displacement parameters in protein crystal structures

“…Atomic displacement parameters (ADPs, often referred to as thermal or B factors) are given increasing signi®cance in protein crystallography since they provide information on thē exibility of main-chain and side-chain atoms when anisotropically (Dauter et al, 1995;Longhi et al, 1997;Harata et al, 1998) or isotropically (Carugo & Argos, 1997Luedemann et al, 1997) re®ned. The ADPs are also useful to infer the precision of atomic positional coordinates (Murshudov & Dodson, 1997;Cruickshank, 1996) and to provide a statistical basis for comparing different structural results (Carugo & Eisenhaber, 1997;Peters-Libeu & Adman, 1997). The best predictions of the¯exibility of a polypeptide chain have been based on analyses of ADPs in known structure test sets (Karplus & Schulz, 1985;Bhaskaran & Ponnuswamy, 1988;Vihinen et al, 1994;Parthasarathy & Murthy, 1997.…”

“…The ADPs are also useful to infer the precision of atomic positional coordinates (Murshudov & Dodson, 1997;Cruickshank, 1996) and to provide a statistical basis for comparing different structural results (Carugo & Eisenhaber, 1997;Peters-Libeu & Adman, 1997). The best predictions of the¯exibility of a polypeptide chain have been based on analyses of ADPs in known structure test sets (Karplus & Schulz, 1985;Bhaskaran & Ponnuswamy, 1988;Vihinen et al, 1994;Parthasarathy & Murthy, 1997.…”

Comparing anisotropic displacement parameters in protein structures

“…One could alternatively compare the electron-density distributions in real space, including both positional and thermal parameters. This approach was taken by Peters-Libeu & Adman (1997) to compare the immediate environment of metal centers among multiple protein structures, although in that case the atoms were modeled using only a single isotropic displacement parameter.…”

A normalized root‐mean‐spuare distance for comparing protein three‐dimensional structures

“…Quantitative comparison of three-dimensional structures is a fundamental task in structural biology (Carugo and Eisenhaber 1997;Peters-Libeu and Adman 1997), especially in such fields as domain fold classification and structural evolution studies (Domingues et al 2000;Yang and Honig 2000). A very popular quantity used to express the structural similarity is the root-mean-square distance (rmsd) calculated between equivalent atoms in two structures, defined as…”